Question

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$,

Answer 1

v = 40/3

Answer 2

We are given the lens equation

$$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$$

with the values

$$u = -40,\quad f = +10.$$

Substitute the values into the equation:

$$\frac{1}{v} - \frac{1}{-40} = \frac{1}{10} \quad\Longrightarrow\quad \frac{1}{v} + \frac{1}{40} = \frac{1}{10}.$$

Rearrange to solve for $\frac{1}{v}$:

$$\frac{1}{v} = \frac{1}{10} - \frac{1}{40} = \frac{4-1}{40} = \frac{3}{40}.$$

Taking the reciprocal gives:

$$v = \frac{40}{3}.$$

Minimal Explanation: Substitute $u=-40$ and $f=10$ in $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$ to get $\frac{1}{v} = \frac{1}{10} - (-\frac{1}{40}) = \frac{3}{40}$ so $v=\frac{40}{3}$.